Added "Somewhat Random Numbers"

Reviewed-on: #5
Co-authored-by: Mark <mark@betalupi.com>
Co-committed-by: Mark <mark@betalupi.com>

authors.toml

@@ -1,3 +0,0 @@
-[authors."mark"]
-email = "mark@betalupi.com"
-webpage = "betalupi.com"

lib/typst/local/handout/0.1.0/handout.typ

@@ -137,7 +137,11 @@
   }
 }
 
-#let notsolution(content) = {
+#let if_solutions(content) = {
+  if show_solutions { content }
+}
+
+#let if_no_solutions(content) = {
   if not show_solutions { content }
 }
 

src/Advanced/Tropical Polynomials/parts/00 arithmetic.typ

@@ -126,7 +126,7 @@ Fill the following tropical addition and multiplication tables
 
 #let col = 10mm
 
-#notsolution(
+#if_no_solutions(
   table(
     columns: (1fr, 1fr),
     align: center,

src/Advanced/Tropical Polynomials/parts/01 polynomials.typ

@@ -63,7 +63,7 @@ where all exponents represent repeated tropical multiplication.
 Draw a graph of the tropical polynomial $f(x) = x^2 #tp 1x #tp 4$. \
 #hint([$1x$ is not equal to $x$.])
 
-#notsolution(graphgrid(none))
+#if_no_solutions(graphgrid(none))
 
 #solution([
   $f(x) = min(2x , 1+x, 4)$, which looks like:
@@ -132,7 +132,7 @@ How can we use the graph to determine these roots?
 Graph $f(x) = -2x^2 #tp x #tp 8$. \
 #hint([Use half scale. 1 box = 2 units.])
 
-#notsolution(graphgrid(none))
+#if_no_solutions(graphgrid(none))
 
 #solution([
   #graphgrid({
@@ -210,7 +210,7 @@ and always produces $7$ for sufficiently large inputs.
 #problem()
 Graph $f(x) = 1x^2 #tp 3x #tp 5$.
 
-#notsolution(graphgrid(none))
+#if_no_solutions(graphgrid(none))
 
 #solution([
   The graphs of all three terms intersect at the same point:
@@ -261,7 +261,7 @@ How are the roots of $f$ related to its coefficients?
 #problem()
 Graph $f(x) = 2x^2 #tp 4x #tp 4$.
 
-#notsolution(graphgrid(none))
+#if_no_solutions(graphgrid(none))
 
 #solution(
   graphgrid({

src/Advanced/Tropical Polynomials/parts/02 cubic.typ

@@ -10,7 +10,7 @@ Consider the polynomial $f(x) = x^3 #tp x^2 #tp 3x #tp 6$. \
 - use this graph to find the roots of $f$
 - write (and expand) a product of linear factors with the same graph as $f$.
 
-#notsolution(graphgrid(none))
+#if_no_solutions(graphgrid(none))
 
 #solution([
   - Roots are 1, 2, and 3.
@@ -48,7 +48,7 @@ Consider the polynomial $f(x) = x^3 #tp x^2 #tp 6x #tp 6$. \
 - use this graph to find the roots of $f$
 - write (and expand) a product of linear factors with the same graph as $f$.
 
-#notsolution(graphgrid(none))
+#if_no_solutions(graphgrid(none))
 
 #solution([
   - Roots are 1, 2.5, and 2.5.
@@ -82,7 +82,7 @@ Consider the polynomial $f(x) = x^3 #tp 6x^2 #tp 6x #tp 6$. \
 - use this graph to find the roots of $f$
 - write (and expand) a product of linear factors with the same graph as $f$.
 
-#notsolution(graphgrid(none))
+#if_no_solutions(graphgrid(none))
 
 #solution([
   - Roots are 2, 2, and 2.

src/Warm-Ups/Odd Dice/meta.toml

@@ -4,8 +4,3 @@ title = "Odd Dice"
 [publish]
 handout = true
 solutions = true
-
-[[attribution]]
-who = "mark"
-when = 2024-02-13
-what = "Initial version of handout"

src/Warm-Ups/Somewhat Random Numbers/main.typ

@@ -0,0 +1,81 @@
+#import "@local/handout:0.1.0": *
+
+#show: doc => handout(
+  doc,
+  quarter: link(
+    "https://betalupi.com/handouts",
+    "betalupi.com/handouts",
+  ),
+
+  title: [Somewhat Random Numbers],
+  by: "Mark",
+)
+
+#problem()
+Alice generates 100 random numbers uniformly from $[0,1]$. \
+Bob generates 101 random numbers from $[0, 1]$, but deletes the lowest result.
+
+#v(2mm)
+
+Say we have both of the resulting arrays, but do not know who generated each one. \
+We would like to guess which of the two was generated by Bob. \
+What is the optimal strategy, and what is its probability of guessing correctly?
+
+
+#solution([
+  Looking at the mean seems like a good idea, but there's a better way: \
+  Assign the array with the smaller _minimum_ to Alice.
+
+  #v(3mm)
+
+  To compute the probability, generate 201 numbers. \
+  Assign the first 100 to Alice and the rest to Bob. \
+  Look at the lowest two numbers (of these 201, *before* Bob drops his lowest).
+
+  #v(8mm)
+
+  We'll use the following notation: \
+  `AB` means the lowest was owned by Alice, and the second-lowest, by Bob.
+
+  #v(2mm)
+
+  Probabilities are as follows: \
+  - `AA`: $100\/201 times 99\/200 approx 0.246$
+  - `AB`: $100\/201 times 101\/200 approx 0.251$
+  - `BA`: $101\/201 times 100\/200 approx 0.251$ // spell:disable-line
+  - `BB`: $101\/201 times 100\/200 approx 0.251$
+
+  #v(4mm)
+  Now, Bob drops his lowest number. \
+  We'll cross out the number he drops and box the new lowest number (i.e, the one we observe):
+  - #{
+      (
+        box(`A`, stroke: ored, inset: 1pt)
+          + box(`A`, inset: 1pt)
+          + box([: $approx 0.246$], inset: (top: 1pt, bottom: 1pt))
+      )
+    }
+  - #{
+      (
+        box(`A`, stroke: ored, inset: 1pt)
+          + box(strike(`B`), inset: 1pt)
+          + box([: $approx 0.251$], inset: (top: 1pt, bottom: 1pt))
+      )
+    }
+  - #{
+      (
+        box(strike(`B`), inset: 1pt)
+          + box(`A`, stroke: ored, inset: 1pt)
+          + box([: $approx 0.251$], inset: (top: 1pt, bottom: 1pt))
+      )
+    }
+  - #{
+      (
+        box(`B`, stroke: ored, inset: 1pt)
+          + box(strike(`B`), inset: 1pt)
+          + box([: $approx 0.251$], inset: (top: 1pt, bottom: 1pt))
+      )
+    }
+  #v(8mm)
+  Alice has the smallest number in 3 of 4 cases, which have a total probability of $approx 0.749$.
+])

src/Warm-Ups/Somewhat Random Numbers/meta.toml

@@ -0,0 +1,6 @@
+[metadata]
+title = "Somewhat Random Numbers"
+
+[publish]
+handout = true
+solutions = true